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We calculate the Josephson current between two one-dimensional (1D) nanowiresoriented along $x$ with proximity induced $s$-wave superconducting pairing andseparated by a narrow dielectric barrier in the presence of both Rashbaspin-orbit interaction (SOI) characterized by strength $\alpha$ and Zeemanfields ($h$ along $\hat z$ and ${\bf B}$ in the $x-y$ plane). We formulate ageneral method for computing the Andreev bound states energy which allows us toobtain analytical expressions for the energy of these states in severalasymptotic cases. We find that in the absence of the magnetic fields the energygap between the Andreev bound states decreases with increasing Rashba SOIconstant leading eventually to touching of the levels. In the absence of RashbaSOI, the Andreev bound states depend on the magnetic fields and displayoscillatory behavior with orientational angle of B leading to magneto-Josephsoneffect. We also present analytic expressions for the dc Josephson currentcharting out their dependence on ${\bf B}$, $h$, and $\alpha$. We demonstratethe existence of finite spin-Josephson current in these junctions in thepresence of external magnetic fields and provide analytic expressions for itsdependence on $\alpha$, $\bf B$ and $h$. Finally, we study the AC Josephsoneffect in the presence of the SOI (for $|{\bf B}|=h=0$) and an externalradiation and show that the width of the resulting Shapiro steps in such asystem can be tuned by varying $\alpha$. We discuss experiments which can testour theoretical results.

Effect of Magnetic Field and Rashba Spin-Orbit Interaction on the Josephson Tunneling between Superconducting Nanowires